"I remember David Moyes a couple weeks ago saying United did so well after losing at Anfield. But when you lose a game of this magnitude I sometimes feel you have to say that you've lost - it is that important a game that you can't look for too many positives - the result has gone for me.
"We can't say Liverpool played poorly tonight, but we shouldn't be looking at it positively. When you go out of a cup competition to Manchester United, you shouldn't be talking about a good performance."
The loss makes it two in as many games for Liverpool and Carragher believes the goal they conceded was down to small mistakes.
"When you talk about big games like this, it's about the small things and Jose Enrique has lost his man at the corner for the goal and then game over, you're out of the cup.
"They played a different system; it worked to a certain extent. Suarez and Daniel Sturridge's partnership looked sharp and together, and the formation looked like it could get the two of them to play, but once you go out of the cup to Manchester United I don't think you should be looking at it and saying 'Liverpool played well... we did this well'."